⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠼⢻⣷⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢃⠐⣏⣟⣸⢣⡆⠀⠀⠀⠐⠳⠃⠉⣥⣆⣠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠤⣬⠍⠉⠁⠆⠀⠀⠀⠨⢼⡄⠜⢿⣭⡼⠋⡦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠲⠆⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣼⣿⣿⣤⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠶⣶⣄⣄⡀⠀⠀⢺⡿⠟⠛⠋⠉⡻⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡯⠿⠽⢆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢰⣿⣷⠌⡿⢻⡃⠀⠀⢋⠀⠀⠀⠀⢰⣼⣤⣽⣿⡯⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢠⢾⣶⡄⢹⠼⢦⠀⠀⠀⠀⠀⠀⠀⠿⠒⡓⠊⠉⠁⡀⣴⡛⠋⠀⢀⠆⠀⠀⠀⠀⢸⣿⣿⣿⣛⣡⣧ ⠀⠀⠀⠀⢀⢠⣠⣠⠀⡀⠀⠀⠀⢻⣌⠋⠛⠚⢁⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠋⠁⠁⠀⠀⠀⠠⣞⠠⣀⠀⠀⠀⠙⢿⣿⣿⣿⡇ ⠀⢠⡴⣿⣿⡿⡄⠹⡑⡕⠀⠀⠀⠀⠛⠛⠒⠋⢉⣦⣦⣞⡢⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡇⠂⠠⠀⡤⠒⠂⠒⠂⠘ ⠈⢭⡣⠳⢯⡵⠃⢠⠱⠼⠀⠀⠀⠀⠀⠀⠀⢠⡿⢹⣝⣻⠇⢸⢱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⠉⠳⠜⠆⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠪⠅⠤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠝⢉⣡⣬⡐⠺⡂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣕⣀⢺⣟⣛⣷⣴⠈ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠬⠀⢠⣾⡯⣷⠀⡳⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠈⠀⠀ ⠀⠀⠀⠾⣷⣾⠿⣛⣶⣟⡷⠦⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣻⣛⠛⠍⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠰⣅⠀⣼⣟⣿⣿⠿⡆⠈⡹⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣥⣈⠁⠙⢬⣌⣭⡾⠃⠀⢹⣦⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠧⠉⠛⠢⣄⣤⣠⡀⣠⣤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⠿⠛⢉⣉⣛⡻⢮⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢷⡁⠀⢰⡿⢫⣿⣿⡆⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡀⠀⣄⢠⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡉⠂⠘⢯⣼⣷⡿⠃⢀⠞⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣼⡖⠓⣼⣼⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣵⣤⢠⠀⠀⢠⣤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⠅⠀⠀⢀⠔⠚⣶⣾⡽⣞⣤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣼⡿⣷⣾⣷⣆⠰⣿⡷⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⢹⡥⣌⠟⠛⠁⡜⣿⠀⢰⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠙⠾⣦⠶⣦⢞⡁⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀